8.1 AreaCurves Between - STEM Math & Calculus · This was created by Keenan Xavier Lee, 2013. See my website for more information, lee-apcalculus.weebly.com. KDT Finding Area using

This was created by Keenan Xavier Lee, 2013. See my website for more information, lee-apcalculus.weebly.com.

8.1 Area BetweenCurves

Standards :

MCI 1

MCI 1c


KDT Finding Area using Integration

Let's consider the function ftxkx'+2

.Find the area between X - 1 & x = 2

.

j#€T¥¥¥¥¥inY¥tr5Iw¥n9e¥ang%¥h¥g:13+2 dx : IT +2×3,2=[421+214] - [HIT ZHD =[8) - [-1.7-5]

= 9.75.

n@ Area between Curves

Let's consider 2 functions : fkl Igk ).

We want to find the area between2 arbitrary curves

.

tEtµ*ff*.

It"±E" "

zfuteraesundef;IfH.glx⇒WHEEL.

*!⇒±kbe*o±r

.


Example 'D Find

.thearea under the canes

.

y=x2 pat') . [xD dx = § x't

- xzdx

¥ y=rx'

= }xI§}=GH" ' H'

) - [D

f*a¥*e= :* .

i.Nixa¥×4 . ×

O=×(x3 - 1)×=O

,1

Example Bend the area between the curves y=O&y=R between XO and* '

{ rx'. odx :{ x "dx=}x "

µ#t*Y×.net#*g.Ery

\o '

z = 2¥.


Example D Find the area between y= - x & y = 2×2.

j#¥¥¥¥e*¥I¥E¥oa- xy - f- D dx = } 2 - it xdx = 2x'§ + x÷ }

= [24 . ¥ + ¥) - fth - t¥ + EID= [4 -

§ +42- [-2 + } - I ]= 4 +2 - § . t + I - tz

= 6 -

§ + 2 - I= 6 - 3 +2 - I

= S - { = 4@


[Exampled Findtheareaofcurvesboundedbyyixr ,y=Oandy=x -2.

Tjx-2

Area At ARAB

y=rx Arena :& Cotto ]d×

.µ¥M Arab :{ # . G-Ddx

¥*E*k*µ*: :* .

Hofnish ,evaluate both integrals &

Ladd the results

. )

××?[0 HYEH-2¥/-2¥12-4×+40=6-5×+4

0=1×-411×-1)

O=×=4,*


Now let's consider the 2 equations : x = fly ) and x : gay).

÷EE¥EF¥H*"⇐I¥i¥H÷t¥wt¥¥a¥

*,¥¥Io±¥think

Example D Find the area between curves .

I'⇒tE÷E:#.ie?iE:.tHEKiHEEIIn

.

= 4 - 3 - } t I

= 2 - } = j6 - } =±f

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8.1 AreaCurves Between - STEM Math & Calculus · This was created by Keenan Xavier Lee, 2013. See my website for more information, lee-apcalculus.weebly.com. KDT Finding Area using